General

Axial Capacity

Piles are structural members that are used to provide capacity by distributing loads throughout a soil mass which can resist loads applied in the direction of the vertical axis of the pile. They can gain this capacity by skin friction along the walls of the pile, or by end bearing pressure on the end of the pile (either on the pile annulus or the full end area). Sometimes they both provide capacity, and sometimes it is one or the other. Piles can also provide resistance to uplift (tension) loads by only mobilising skin friction resistance.

OPILE considers that pile axial capacity can be gained in three ways:

  1. Plugged Capacity comprises of external skin friction + full end bearing.

  2. Unplugged Capacity comprises of external + internal skin friction + annular end bearing.

  3. Tension Capacity which only comprises of external skin friction.

The skin friction and end bearing can be calculated according to various axial methods , both industry established and more contemporary, depending on the available soils data and the soil type. The TZ & QZ curves are determined using similar shapes for each, regardless of the method selected.

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Length Dependent Axial Methods

Certain axial capacity methods contained in OPILE are length dependent (e.g. SANDICP & CLAYICP, SANDUWA, CLAYKOLK etc). This means that the distance from the pile tip influences the friction at any point along the pile.

Caution

Some caution should be applied when using length dependent results as the skin frictions and TZ curves that are output are valid for the final penetration only! For any other penetration it will be necessary to rerun OPILE in order to determine the correct curves and skin friction profile.

Under the AxCap tab there two output tables. The first table contains details of all pile capacities for “final tip penetrations” between 0m and the final penetration and they are output for the bottom of each pile element. These capacities account for length effects, where necessary, and are used on the plots. They are also comparable to the results produced by ALLCAP.

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The second AxCap table produces details of the capacity for the final penetration (skin friction, end bearing pressures and incremental frictions) and allows for cross checking with the axial finite element analyses. It is also possible to cross check the output from this table with the final capacities in the first table, should more detail be required.

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Axial Analysis

The axial response of a pile depends upon the soil properties and the section properties of the pile. The compression or extension of a pile may be calculated by considering the variation of the axial load, P, down the length of the pile. The variation is given by:

\[\frac{dp}{dz} = -2 \cdot \pi \cdot r_0 \cdot \tau_0\]

Where:

\(r_0\)

is the radius of the pile

\(\tau_0\)

is the shear stress at the pile wall

The axial strain in the pile is then given by:

\[\frac{dw}{dz} = \frac{P}{(E \cdot A) \cdot p}\]

Where:

\(E \cdot A\)

is the axial stiffness of the pile cross section

Combining the two equations above then gives:

\[\frac{d^2 w}{dz^2} = \frac{2 \cdot \pi \cdot r_0 \cdot \tau_0}{E_0 \cdot A_0}\]
\[\frac{d^2}{dz^2}w = \frac{2 \cdot \pi \cdot r_0 }{(E \cdot A) \cdot p}\]

This equation is solved in OPILE using a finite element approach. For combined axial/torsional loading the TZ curves are considered to interact with each other, by considering an equivalent radial displacement, as shown in the figure below. Finnie & Morgan (2004) outlines an approach for considering the torsional loading of conductors.

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Interaction between axial and torsional TZ curves.

For more information on the torsional analysis of piles see Finnie & Morgan (2004). When carrying out torsional analysis QZ curves should not be used as the analysis will not give correct results if they are included.


Mobilised Axial Capacity

The axial pile capacity as presented in the tab ‘AxCap’ is calculated by a combination of shear resistances and end bearing resistance, both of which are defined depending on the selected Axial Capacity methods. Both the shear and the end bearing resistances calculated for the axial pile capacity consider the peak soil strength as input, as such, API RP2GEO (2011) refers to the calculated axial capacity as the ultimate axial capacity. In some circumstances such as when soils exhibit strain-softening behavior and/or the piles are axially flexible, the actual capacity of the pile may be less than the axial pile capacity as presented in the tab ‘AxCap’.

The mobilized axial capacity for tension and compression corresponds to the peak axial capacity provided from pile load-displacement analyses, performed at pile top. For all penetrations:

  • the Mobilized Capacity Compression corresponds to the Intermediate Compression Peak, when present, and to the Ultimate Peak Compression Load, when no Intermediate Peak is present.

  • the Mobilized Capacity Tension corresponds to the Peak Tension Load.

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Lateral Analysis

OPILE carries out lateral analysis of piles by idealising the pile as a beam that is supported by a series of springs distributed along its length, as shown in the figure below. The basic governing equation for this system is:

\[E \cdot I \cdot \frac{d^4 y}{dx^4} + F \cdot \frac{d^2 y}{dx^2} - k \cdot y = 0\]

Where:

E

is the Youngs modulus of the pile material

I

is the second moment of area of the pile

Y

is the lateral deflection of a particular point on the pile

x

is the distance from the pile head

k

is the spring stiffness

F

is an applied axial load to account for the p-d effect

The springs for this type of analysis are generally non-linear and are called PY curves. Where P is a lateral pressure and Y is a displacement at which that pressure is mobilised. In order to solve laterally loaded pile problems OPILE uses an iterative approach. Reese & Van Impe (2001) contains extensive guidance on lateral pile analysis.

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Soil Resistance to Driving

When piles are driven the experience resistance from the ground, this is known as Soil Resistance to Driving (SRD). SRD is calculated in a similar way to axial capacity. However, SRD is often calculated with upper bound soil strength profiles and gives in a number of different results to account for upper and lower bound driving resistance. The results of the SRD calculations provide input for use in GRLWEAP or other similar pile driveability programs.

The SRD is usually calculated by a combindation of skin friction and end bearing. OPILE does not differentiate between internal and external skin friction. However, where applicable skin friction factors are provided so that internal and external skin friction can be controlleded. For example a factor of 1.5 would be used to provide full external friction and 50% of the internal skin friction.

OPILE will calculate end bearing based upon the recommendations of the method and this will include plugged and unplugged end bearing. Note, that for the purposes of SRD unplugged end bearing is only based upon the annualar area of the pile, unlike the calculations for axial capacity where unplugged end bearing capacity may include internal skin friction. Plugged end bearing is based upon the full area of the pile.

The effect of a pile driving shoe is discussed in the relevant section.

For information on the implementation of the different SRD methods can be found in the SRD Input section.


Pile Dimensions & Makeup

Pile penetration and length are considered as two different dimensions in OPILE. Pile penetration specifies the depth of the pile tip below mudline, whereas pile length specifies the actual length of the pile. If the pile length is greater than the pile penetration then this means that some of the pile defined will remain above mudline. Currently it is not possible to analyse a pile where the pile head is below mudline, it is suggested that the users should adjust the local Scour depth or the soil input parameters to account for this.

It is necessary to define sufficient pile sections to cover the length of the pile that is to be analysed, from the pile head to the pile tip. Note that when inputting dimensions some unit conversions have been included by the addition of a key, see the Units_Convention section for more information.

Pile makeup is the term used to describe the series of pile sections that make up the pile. Each section is defined by a top and bottom depth and possesses a series of dimensions and properties including the diameter, wall thickness and material number. The material number is used to define which material from the material input table is used. The pile dimensions are described below:

It is always recommended that the pile is reanalysed once the final pile make up and configuration is selected to ensure that the correct pile sections and material properties are used.

Top & Bottom Depth

The top and bottom depth specify the start and end of the section on the pile. They are specified as distances in metres from the pile head. Obviously the bottom depth must be greater than the top depth.

Diameter

Diameter is the outer diameter, in metres, of the pile for a particular pile section. The outer diameter can be varied along the pile and the pile response curves (PY, TZ & QZ) are calculated to take account of such variations. For instance it is possible to analyse a pile which has a larger diameter at the top as this could be an efficient way to design piles which have large lateral loads.

Wall Thickness

The wall thickness of the pile is defined in metres and the wall thickness should always be less than half of the pile outer diameter, otherwise an error will occur and OPILE will not analyse.

Pile Section & Pile Weight

Pile section and total pile weight are calculated automatically from the pile dimensions and material unit weights that are input. If a material weight greater than zero is defined there remains an option as to whether the pile weight will be included in the axial finite element analysis, or not. The effect of pile weight is not included in lateral analysis.

OPILE is based upon hollow tubular piles, therefore other section types (such as concrete piles) cannot be input directly. It would require some conversion of pile section properties to come up with an equivalent tubular pile. Support of other pile sections may be included in OPILE at a later date.

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Scour

Scour in OPILE is considered to comprise of two different components: general scour and local scour, which are illustrated in the figure below.

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General scour arises from overall seabed erosion, whereas local scour is considered to affect a much smaller region, within a few diameters of a pile and may involve a steep sided scour pit. Local scour could also be used to include a depth where loss of contact (gapping) occurs between the pile and soil and can be used to model very localised effects around individual piles. OPILE offers full control over how scour can be accounted for within the calculations. Scour principally affects the overburden pressure, which has consequent effects on the axial and lateral response curves that are generated. Within the general scour zone the overburden pressure is automatically set to zero, as are the axial and lateral resistances, regardless of what any particular method might allow.

If neither general or local scour is specified then the overburden pressure remains unmodified. If a general scour is specified, but no local scour, then the overburden pressure is reduced by the amount which would have been gained over the depth of general scour.

If a non zero local scour zone is specified then an overburden reduction depth must also be specified and between this zone the overburden makes a transition, over the overburden reduction depth, from zero overburden pressure up to the overburden pressure with general scour, as shown in the figure below. Within the overburden reduction depth the overburden pressure is interpolated. An example of the overburden calculation is shown in the figure below and OPILE shows the results of overburden calculations under the axial capacity tab.

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Pile Materials

The pile material has various properties that are attributed default values in OPILE to give quick input for the material properties of steel. However, they can be modified for individual analyses by changing the properties in the pile materials table as seen in the figure below.

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Up to 10 pile materials can be specified and not all materials that are specified have to be used.

Young’s Modulus

The Young’s modulus is used in the axial and lateral finite element analysis and a typical value for steel is 205000000kPa.

Poisson’s Ratio

The Poisson’s ratio of the material is defined in this column, typically for steel the Poisson’s ratio is about 0.3.

Yield Stress

The yield stress is not directly used in any calculations. It is used in the presentation of results of Lateral Analysis. Yield stress has no effect on the apparent load that a pile may take. It is left to the user to interpret the results and to check that the yield stress has not been exceeded. The results of Lateral Analysis do present the stress in the pile and provide summaries of the maximum stress for any particular load case, thus allowing easy checking.

Pile Material Unit Weight

This is the unit weight of the pile material and is defined in kN/m 3. Typical values of unit weight for steel are about 78kN/m 3 however this should be adjusted to account for the fact that the material is underwater, making 68kN/m 3. The material unit weight is not used in calculation of axial capacity, however the option does exist to use it in the axial load-displacement analysis.


Pile Grid

Pile grids in OPILE are used in the generation of response curves and then in any subsequent finite element analysis. Separate grids are used for the axial and lateral analysis and the grids can be found under the custom input tab. OPILE will automatically generate grids, based on a user specified maximum grid spacing, however they can also be input by the user. Generally it will be easier to use the automatic grid generation.

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Generated grids take into account any pile stickup, scour and local scour. However, pile stickup is not included in the axial analysis as it will have no effect. The SRD grid never accounts for scour as this would not be valid for such a short term situation. In addition any stratigraphy changes that are encountered within the axial or lateral soil input are taken into account. This may be particularly important for shallow soils in PY analysis, or stratigraphies which are defined near the pile tip for axial analysis. OPILE is limited to 200 grid points on a pile which is likely to be sufficient for all situations (100 grid points for all OPILE versions before 1.7.0.1).

The primary input for pile grid generation is to specify a minimum distance between grid points, the default value is 1m, however anything between 0.5 to 2m would be acceptable. The pile grids are subject to the constraint of a maximum of 200 points. During grid generation, if OPILE finds it will miss the bottom of a soil stratigraphy it will insert an additional grid point in order that no detail within the soil stratigraphy definition is missed out.

The grid points are used to define beam elements which consist of a top and bottom depth. Each beam element has a uniquely calculated response curve (i.e. TZ, QZ or PY curve) attached to it. These defined beam elements are then used in any subsequent finite element analysis.


Analysis Options

When the “Analyse” button is pressed OPILE starts an analysis routine. Precisely what is carried out within this routine is controlled by the user options within the tab ‘Analyses’ under the general tab. In some cases options may not be available if another option is not selected. For example it is not possible to carry out Lateral load displacement response without using the option to generate PY curves. This particular case would only be allowed when the checkbox ‘Do not generate TZ, QZ and PY Curves’, found in the tab ‘Analyses Options’ is checked.

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Within the options there are “parent” options and “child” options. For example, if an option does not appear to be enabled (such as the Lateral Load Displacement Response above) then this means other options must first be selected to enable it. If an option is disabled but the check box is in a checked state then the option will not be included in the analysis.

Conductor Mode

The conductor mode in OPILE is used for analysing conductor piles and other piles that are subjected to torsional loads. If the conductor mode check box is checked then no end bearing or QZ curves are calculated, thus end bearing will not be used in the finite element analysis.

Response Analysis Options

Do not generate TZ, QZ and PY Curves. The generation of TZ and QZ curves can be uncoupled from the axial load displacement analysis. If an axial load displacement analysis is performed without recalculation of TZ, QZ curves and axial capacity, the following input is necessary:

  • AxCap (All Penetrations)

  • AxCap Details (Final Penetration)

  • TZ Curves (Compression only - the tension T values are derived from the ‘AxCap’ Details, column ‘Tens Mod’)

  • QZ Curves

The generation of PY curves can be uncoupled from the lateral load displacement analysis. If a lateral load displacement analysis is performed without recalculation of the PY curves, the following input is necessary:

  • Cyclic PY curves - in case “CYCLIC” was selected as lateral analysis case in the Lateral Input tab.

  • Static PY curves - in case “STATIC” was selected as lateral analysis case in the Lateral Input tab.

Iteration Limit for Load Displacement Analyses. The finite difference problems are solved iteratively until the soil stiffness and pile displacement remain unchanged and the iteration limit controls the number of iterations which are allowed, before the calculation will finish. Typically about 10 to 20 iterations are required to solve a problem, sometimes more than this, therefore the iteration limit has a default value of 100.

Mobilised Capacity Options

The Mobilized Capacity Options are only relevant for the generation of the mobilized capacity output that is outputted in the tab ‘AxMobCap’.

Detailed description of the Mobilised Capacity Options are addressed in the Axial Mobilised Capacity Input page.